A binary message (0 or 1) is transmitted through a noisy channel. Let X be the message transmitted, and let Y be the message received. Suppose that X = 0 and X = 1 is transmitted with equal probability and suppose that the receiver obtains the message correctly 90% of the time. Determine the joint PMF of X and Y. P(X = 1, Y = 0) Choose... Choose... P(X = 0, Y = 1) 0.40 0.45 P(X = 1, Y = 1) 0.10 0.05 P(X= 0, Y = 0) Choose...

A digital communication channel transmits bits of information, usually designated as 0 and 1. If a sender transmits a 0, he/she hopes the recipient receives a 0. If a sender transmits a 1, he/she hopes that the recipient receives a 1. Unfortunately, this is not always the case. Suppose on a certain transmission line, a transmitted 0 is received correctly 90% of the time (10% of the time a 1 is received), and a transmitted 1 is received correctly 74% of the time. (26% of the time a 0 is received.) It is known that on this transmission line, 80% of all bits transmitted are 0 bits.A randomly selected transmitted bit is examined. Say its value is X. The bit received is Y.a.What is the probability that X = 0? b.What is the probability that X = 0 and Y = 0? c. What is the probability that X = 1 and Y = 0? d. What is the probability that Y = 0? e. What is the probability that X = 0 given that Y = 0? f. If 1000 random transmitted bits are examined, what is the expected number of 0 bits in this…

About 7% of messages on Jmes.com have objectionable material. This means that if we randomly select a Jmes.com message there is a probability 0.07 that the message will be objectionable. Whether one message has objectionable material is independent of whether any other message has objectionable material. Suppose we randomly select Jmes.com messages, one by one. Let X = the number of non-objectionable messages we select until we select our 1st objectionable message. Let Y = the number of non-objectionable messages we select until we select our 3rd objectionable message.a. What is the probability that the 1st two messages selected are non-objectionable? b. What is the expected value of X? c. What is the variance of X? d. What is the probability that X > 13? e. What is the probability that X ≤ 13? f. What is the probability that Y = 40? g. What is the probability that Y ≤ 40? Add any comments below.

i am not understanding how the probability of part C is found

Give three examples of Bernoulli rv's (other than those in the text). (Select all that apply.) Ox = 1 if a randomly selected shopper purchases a food item at a department store and X = 0 otherwise. Ox = the number of lightbulbs that needs to be replaced in a randomly selected building and x = 0 if there are none. Ox = 1 if a randomly selected lightbulb needs to be replaced and X = 0 otherwise. Ox = the number of food items purchased by a randomly selected shopper at a department store and X = 0 if there are none. Ox = 1 if a randomly selected day has a high temperature of over 100 degrees and X = 0 otherwise. Ox = the number of days in a year where the high temperature exceeds 100 degrees and X = 0 if there are none.

Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer wras started in order to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who vwere diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease. A USE SALT (a) If you wish to determine whether the community screening program has been effective, state the alternative hypothesis that should be tested. O Hgip + O H;: p > O H: p= O Hgi p O Ho: P = O Hoi p * (c) If 194 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using a = 0.05. Find the test statistic and the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)…

Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume that failures of different links are independent. Link 1 A Link 3 Link 2 Link 4 Link 5 B (a) Assume that p = 1/3. Find the probability that there exists a path from A to B along which no link has failed. (b) Given that exactly one link in the network has failed, find the probability that there exists a path from A to B along which no link has failed

In an area having sandy soil, 40 small trees of a certain type were planted, and another 40 trees were planted in an area having clay soil. Let X = the number of trees planted in sandy soil that survive 1 year and Y = the number of trees planted in clay soil that survive 1 year. If the probability that a tree planted in sandy soil will survive 1 year is 0.5 and the probability of 1-year survival in clay soil is 0.4, compute an approximation to P(-4 < X – Y < 4) (do not bother with the continuity correction). (Round your answer to four decimal places.) In USE SALT .148

Suppose X and Y have the joint probability distribution given by the table shown below. Compute Cov(X,Y). -0.750 O-0.125 -0.625 -0.250 -2 y o 2 0 18 1 BIT 8 x 1 1 4 1 2 0

A computer disk storage device has ten concentric tracks,numbered 1, 2,…, 10 from outermost to innermost, and asingle access arm. Let pi 5 the probability that any particularrequest for data will take the arm to tracki(i 5 1,… , 10). Assume that the tracks accessed in successiveseeks are independent. Let X 5 the number of tracksover which the access arm passes during two successiverequests (excluding the track that the arm has just left, sopossible X values are x 5 0, 1, …, 9). Compute the pmfof X. [Hint: P(the arm is now on track i and X 5 j) 5P(X 5 j|arm nowon i) ? pi. After the conditionalpro bability is written in terms of p1,…, p10, by the law oftotal probability, the desired probability is obtained bysumming over i.]